The Henig efficient solution under the improved set unifies the Henig efficient solution and the approximate Henig efficient solution, and its stability analysis is indispensable in the numerical calculation. Set-valued optimization problem is a hot problem in the field of optimization. The study of the stability of E-Henig efficient solutions for set-valued optimization problems based on improved sets is of great theoretical and practical importance. Firstly, the E-Henig effective solution of the set-valued optimization problem was introduced based on the concept of improved set and the approximate Henig effective solution and Henig effective solution of the set-valued optimization problem were unified. Secondly, the closed convexity, boundedness and related properties of the recovery cone of the level set of the set-valued mapping were established by using Painlevé-Kuratowski convergence in the case where both the objective mapping and the constraints of the set-valued optimization problem were perturbed. Then, with the obtained closed convexity, boundedness, and properties of recovery cone of the level set of set-valued mapping, stability results for the E-weakly effective point set, the E-Henig effective point set and the E-Henig effective solution for strictly proper quasi C-convex set-valued optimization problems were established, respectively, under the perturbation of both the objective mapping and the constraints of the set-valued optimization problem. The results obtained for the first time focus on the stability results of the set-valued optimization problem based on the weak effective point set, Henig effective point set and Henig effective solution set under the concept of improved set. Compared with the previous literature, which mainly focused on the existence, optimality condition and duality property of Henig effective solutions for set-valued optimization problems, this study has significantly improved the theoretical results of Henig efficient solution for set-valued optimization problems and provided methods and techniques for stability analysis of numerical computations.